Internal problem ID [6707]
Book: Second order enumerated odes
Section: section 2
Problem number: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\tan \relax (x ) y^{\prime }+\left (\cos ^{2}\relax (x )\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.102 (sec). Leaf size: 15
dsolve(diff(y(x),x$2)+tan(x)*diff(y(x),x)+cos(x)^2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (\sin \relax (x )\right )+c_{2} \cos \left (\sin \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 18
DSolve[y''[x]+Tan[x]*y'[x]+Cos[x]^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 \sin (\sin (x))+c_1 \cos (\sin (x)) \\ \end{align*}